Adaptive control of straight worms without derivative measurement

In this paper we consider an adaptive control problem of finite DoF worm-like locomotion systems (WLLS) which contact the ground with Coulomb dry friction. Using a rough mathematical friction law the system is shown to belong to a system class that allows adaptive control. Gaits from the kinematic theory can be tracked by means of adaptive controllers. For this we introduce two different adaptive controllers for λ-tracking and focus on that one which is not based on the derivative of the output. We pay attention to the analysis of such systems and present some theoretical control investigations including proofs. Numerical simulations of tracking different reference signals under arbitrary choice of the system parameters demonstrate and illustrate that the introduced simple adaptive controllers work successfully and effectively. Current experiments are aimed at the justification of theoretical results.